The Optimal Mix of Bank and Market Debt An Asset Pricing Approach Dirk Hackbarth Christopher A Hennessy Hayne E Leland February 5 2003 ABSTRACT This paper examines the optimal mix and priority structure of bank and market debt using a tax shield bankruptcy cost tradeo model where the only unique feature of banks is their ability to renegotiate Closed form expressions are derived for the values of renegotiable bank debt non renegotiable market debt equity and levered firm values Optimal debt structure hinges upon ex post bargaining power Weak firms utilize bank debt exclusively Strong firms use a mixture of bank and market debt with bank debt senior The model explains i why small firms use bank debt exclusively ii why large firms employ mixed debt financing iii why bank debt is senior and iv why firms shift from bank debt into a mixture of market and bank debt over their life cycle The optimal debt contracts entail Absolute Priority and we provide estimates of the cost of ex post priority violations across creditor classes JEL Codes G13 G32 G33 Keywords Banking Capital Structure Priority Structure and Contingent Claims Pricing Walter A Haas School of Business U C Berkeley We would like to thank seminar participants at the University of Arizona U C Berkeley and Stanford University where early versions of this paper were presented Special thanks to Paul Pfleiderer for detailed comments and suggestions I Introduction Following Modigliani and Miller s 1958 irrelevance result the corporate tax shield provided by debt was cited as an important determinant of capital structure More recently contract theorists have questioned the utility of the tax shield in resolving the capital structure puzzle For instance Hart and Moore 1995 argue that these approaches cannot explain the types of debt claims observed in practice 1 This paper demonstrates that reports of the tax shield s demise are premature and that in fact the debt tax shield is su cient to explain many of the stylized facts with respect to debt structure that are central to the banking and contracting literatures The optimal debt structure maximizes ex ante firm value Employing a continuous time asset pricing framework we paper identify the optimal priority structure and mixture of renegotiable debt bank and privately placed debt and non renegotiable market debt 2 Debt mix and priority structure determine the value of tax shields bankruptcy costs and renegotiation costs Analytical solutions are derived for bank debt market debt equity and levered firm values as functions of the endogenous variables promised coupons and priority structure and exogenous parameters ex post bargaining power underlying volatility tax rates renegotiation costs and bankruptcy costs Absolute Priority AP across creditor classes is optimal in our setting and we estimate the ex ante costs of anticipated deviations from AP across creditor classes Optimal debt structure hinges upon the division of ex post bargaining power between the firm and bank We consider two polar cases Strong Firms have full bargaining power in renegotiations and engage in strategic default making take it or leave it o ers over debt service and capturing all bilateral surplus 3 In contrast Weak Firms receive take it or leave it o ers from the bank in renegotiations implying the bank extracts all bilateral surplus For this reason we label the bank debt obligations of strong and weak firms Equity Power Debt EPD and Bank Power Debt BPD respectively In the model firms can choose the optimal mix of market and bank debt but cannot choose the type of bank debt they issue That is in terms of their bank debt commitments strong and weak firms are constrained to issue EPD and BPD respectively Bargaining power is treated as a fact of life for the firm since an agreement to be weak is not incentive compatible 1 Hart 1993 makes the same argument The term bank debt is adopted as a shorthand for all renegotiable debt including private placements 3 The term strategic default is borrowed from Anderson and Sundaresan 1996 and Mella Barral and Perraudin 1997 2 1 ex post It is most natural to think of weak firms as being relatively small or young corporations that are possibly locked into a relationship with a single bank an interpretation consistent with the motivation provided by Rajan 1992 The model generates several predictions that are consistent with the stylized facts First weak firms find it optimal to finance exclusively with bank debt That is for weak firms bank debt dominates any mix of market and bank debt regardless of the priority structure under the proposed mixed debt policy This result holds in the absence of any notion of monitoring or certification by banks transaction costs economies of scale and other common rationales for why small firms fail to tap public debt markets Second the optimal debt structure for strong firms entails a mixture of bank and market debt thus providing a rationale for the coexistence of both types of debt within the capital structure of a single firm Third while employing a mixed debt structure strong firms optimally place bank debt senior in priority To the extent that one views young firms as having a weak ex post bargaining position vis a vis banks and gaining bargaining strength as they mature the model generates a tax based life cycle hypothesis for debt structure Young firms begin by relying exclusively on bank debt As they grow and gain bargaining power they shift away from bank debt placing more reliance on market debt This prediction is consistent with observed financing patterns and is not dependent on bank certification of young firms In fact the model predicts that even if a weak firm could tap public debt markets with fair pricing it would be sub optimal to do so The intuition for our results is as follows First consider optimal debt structure when the firm has full ex post bargaining power Bank debt o ers the advantage of being renegotiable in bad states implying lower bankruptcy costs than those associated with market debt However the strong firm has limited bank debt capacity Since the firm can make take it or leave it o ers to the bank the initial value of bank debt cannot exceed the bank s threat point in renegotiations where the threat point is equal to bank recoveries in the event of reorganization In order maximize its bank debt capacity the strong firm places the bank senior in priority Market debt is shown to complement bank debt Although